Curve goes in different directions
The curve is going in different directions because there are gaps in the curves. In your case there are several point where the curve has a gap. It looks like it is a single continous curve but actually there are 2 end points on top of each other that only make it look like a single curve.
You can fix this by moving on of the overlapping endpoints away form the other and than filling it, use F to connect to points. The direction of the curve will then automatically be normalized. Just to be sure: when you are done with that you can also normalize the curve using Ctrl+N

   

How to find these overlapping points:
To find these point you can in Edit mode, hover of a point with the mouse and hit L. This will select all the connected points. You can than select the end points manually.